Inverse problems of finding the lowest coefficient in the elliptic equation

Alexander I. Kozhanov, Tatyana N. Shipina

Research output: Contribution to journalArticlepeer-review

Abstract

The article is devoted to the study of problems of finding the non-negative coefficient q(t) in the elliptic equation utt + a2∆u − q(t)u = f(x, t) (x = (x1, …, xn) ∈ Ω ⊂ ℝn, t ∈ (0, T ), 0 < T < +∞, ∆ — operator Laplace on x1, …, xn). These problems contain the usual boundary conditions and additional condition ( spatial integral overdetermination condition or boundary integral overdetermination condition). The theorems of existence and uniqueness are proved.

Translated title of the contributionОбратные задачи восстановления младшего коэффициента в эллиптическом уравнении
Original languageEnglish
Article number15
Pages (from-to)528-542
Number of pages15
JournalJournal of Siberian Federal University - Mathematics and Physics
Volume14
Issue number4
DOIs
Publication statusPublished - 2021

Keywords

  • Boundary integral condition
  • Elliptic equation
  • Existence
  • Spatial integral condition
  • Uniqueness
  • Unknown coefficient

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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